Think about the last time you had a revelation -- walking somewhere by yourself, washing yourself in the shower, driving somewhere without the radio on. That's valuable thinking time.
I used to be on Twitter dozens of times a day -- no pictures of the meal I was about to eat, but lots of surfing. I took a two week trip to China, and limited my wireless access to a few times a day for E-Mail only -- the rest of the time I was off the grid. Now I'm back in Canada, I'm continuing that trend -- I've visted Twitter a few times, but my participation is way down. Even riding the subway with my eyes closed is a nice respite from a busy day.
It's important to get your brain some time off.